On Projection Matrices \(\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, \) and their Applications in Computer Vision

摘要

Projection matrices from projective spaces \({\mathcal{P}}^3 {\text{ to }}{\mathcal{P}}^2 \) have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings \({\mathcal{P}}^k \to {\mathcal{P}}^2 ,k = 3,4,5,6\) for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.